Simple tests for analysing and comparing continuously measured data Flashcards
what are the two basic approaches to statistical analysis
Estimation (confidence intervals) Hypothesis testing (p-values)
How do you choose a statistical method
The choice of method of analysis for a problem depends on the comparison to be made and the data to be used
what are 2 common issues
1- Comparison of paired data, e.g. the response of one group under different conditions as in a cross-over trial, or of matched pairs of subjects.
2-Comparison of two independent groups, e.g. groups of patients given different treatments.
what do stat tests types usally fall under
Parametric
Non-parametric
what is an assumption of a para test
Assume data are distributed according to a particular distribution e.g. Normal distribution.
More powerful than non-parametric tests, when the assumptions about the distribution of the data are true.
name some examples of Para tests
t-test, analysis of variance, linear regression techniques
when are non-para methods used
Non-parametric methods are used when:
Data does not seem to follow any particular shape or distribution (e.g. Normal).
Assumptions underlying parametric test not met.
A plot of the data appears to be very skewed.
There are potential outliers in the dataset.
assumptions of non-para tests
data may be skewed, ranked or ordinal
Nonparametric techniques are usually based on ranks or signs.
Robust in presence of potential outliers.
what is the diffrence between Paired or unpaired data
Paired data - same individuals studied at two different times (or individually matched) .
Independent - data collected from two separate groups.
what are some of the assumptions if a paried t-test
The di’s are plausibly Normally distributed. (Note it is not essential for the original observations to be Normally distributed).
The di’s are independent of each other
what are the steps to a parried t-test
1- Calculate differences eg X1i-X2i…. i=1 to n
2- calculate the mean and SD of the diffrences
3- Calculate the standard error of the mean difference
SD/SRT[N]
4-Calculate the test statistic
mean/SE
5-Under the null hypothesis, t is distributed as Student’s t, with n – 1 degrees of freedom
From this you would look on a table to find the p-value
what is the equation for the CI for the mean
the 100(1-a)% CI for mean dif in the pop
Mean-+ (t(df,a) xSE)
, df- defree of freedom, a- sig level (0.05)- use these too find t on the table
what is the Non-parametric equivalent of the paired t-test
Wilcoxon (Matched Pairs) Signed Rank Test
Parametric approach: Independent two-sample t-test for comparing means- assumptions
Two ‘independent’ groups;
Continuous outcome variable;
Outcome data in both groups is Normally distributed ;
Outcome data in both groups have similar standard deviations.
steps in the Independent two-sample t-test for comparing means
1- First calculate the mean difference between groups.
2-Calculate the pooled standard deviation.
3-Then calculate the standard error of the difference between two means.
4-Calculate the test statistic t.
5-Compare the test statistic with the t distribution with
n1 + n2 - 2 degrees of freedom.
6- This gives us the probability of the observing the test statistic t or more extreme under the null hypothesis.
